Question

draw a circle of radius 4cm from a point 12cm away from its centre, construct the pair of tangents to the circle and measure their length

Answer 1

Answer:

The measure of the length of the tangent to the circle from a point outside the circle is:

8√2 cm.

Step-by-step explanation:

The length of the tangent to the circle drawn from a point outside the circle could be calculated with the help of the Pythagorean Theorem.

As the tangent are perpendicular to the circle.

Hence, from the figure we have to find the length of side .AB and AC.

The hypotenuse of the right triangle is the line segment joining the outside point and the center of the circle.

Using Pythagorean theorem in ΔOBA we have:

$OA^2=AB^2+0B^2$

i.e. $12^2=4^2+AB^2\\\\AB^2=12^2-4^2\\\\AB^2=144-16\\\\AB^2=128\\\\AB=8\sqrt{2}$

Similarly we can find the length of the tangent AC.

Hence, the measure of the tangent to the circle is:

8√2 cm.